Random Dynamic Systems


The old saw holds that you are doing well if you get a single new idea from attending an academic conference and I've usually found this to be true.  More often than not, however, the new idea isn't some grand sweeping theory.  It's likely to be a little gimmick, a way of passing out the syllabus or grading a paper.

This past June, for example, I attended the Teaching Professor Conference in St. Louis.  It's a three day teaching geek-fest for profs who want to share pedagogical methods and ideas.  On the first day I did a little workshop on how to get students to pose better questions and then spent the rest of the weekend hitting interesting sounding sessions.

One I attended concerned using improvisational theater techniques in the classroom.  The guy who led it was a former improv comedian turned math professor who uses on-your-feet improv techniques to demonstrate math concepts. Mathematicians, he explained, are very interested in random dynamic systems.  These are systems in motion that contain uncertain or unpredictable elements.  Think of smacking into a hundred tightly packed billiard balls or, for that matter, predicting a stock price.

To demonstrate this idea he asked the 30 people in the audience to stand up and look around the room.  "Pick someone at random but keep your pick to yourself," he said. "This is your secret friend. Now look around and pick someone else. This is your secret enemy.  In a moment I will say go and you must at all times maneuver so your friend is always between you and your enemy."

Within seconds we had created a random dynamic system, a swirling dance of individual persons constantly adjusting to the changing positions of the other people. There was order because there clearly was a set of rules governing our motion, but there was also a bit of chaos because our choices had been randomly selected. Moreover, our motion paths would likely be different each time we played the game.  Even so, mathematicians can actually model these systems using something called stochastic equations.

I loved this way of demonstrating a complex idea and I learned something new, which is saying a lot because my math brain stalled years ago.  I also keep thinking I need to find some way to steal this idea.  That's the thing about teachers.  They're the biggest thieves in the world, but that's okay because an academic conference is really a thieves market.

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